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Definitions. Given sets. Given sets : examples. To introduce declaration of a set of student ; [ student ] In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]. Declaration of variables.

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Definitions

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Definitions


Given sets


Given sets : examples

  • To introduce declaration of a set of student ; [ student ]

  • In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]


Declaration of variables

  • A name is assigned a type when it is declared. Once a given set is declared, we can declare variables.

  • Example

    stud1 : Student --- declaring a student

    library1 : pBook --- declaring a set of books

    primes : p  --- declaring primes to be a set of integers

    newestbook : Book   --- what the book is and a number

    showing the copy

    library : p(Book   ) --- declaring a library as a set of copies of

    books


Abbreviations

  • Syntactic equivalence

  • Example

    basic_ref == {math, intro_to_computers}

  • Is equivalent to the declaration basic_ref : p Book together with

    the predicate basic_ref = {math, intro_to_computers}


Enumerated types

  • Use data type definition to introduce a type with a small number of members

  • Name ::= list of elements separated by |

  • Example

    YesNo ::= yes | no


Axiomatic description

  • To introduce variables along with predicates giving further information


Consistency


Consistency


Consistency : example


Generic Definitions


Generic Abbreviations


Generic Axiomatic Definitions


Generic Axiomatic Definitions


Generic Axiomatic Definitions


Generic Axiomatic Definitions


Characteristic set


Characteristic set


Characteristic set


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